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Properties

Label 555.2.j
Level $555$
Weight $2$
Character orbit 555.j
Rep. character $\chi_{555}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
Newform subspaces $1$
Sturm bound $152$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 555.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(152\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(555, [\chi])\).

Total New Old
Modular forms 160 76 84
Cusp forms 144 76 68
Eisenstein series 16 0 16

Trace form

\( 76 q - 76 q^{4} + 4 q^{5} + O(q^{10}) \) \( 76 q - 76 q^{4} + 4 q^{5} + 4 q^{10} - 8 q^{14} + 76 q^{16} + 32 q^{17} + 4 q^{18} - 8 q^{20} - 16 q^{22} - 4 q^{25} - 16 q^{26} + 16 q^{28} - 28 q^{29} + 16 q^{30} - 8 q^{31} + 4 q^{35} + 56 q^{38} + 4 q^{40} - 40 q^{42} - 8 q^{45} - 96 q^{46} - 16 q^{48} - 12 q^{50} - 8 q^{51} + 12 q^{53} - 24 q^{55} + 72 q^{56} + 76 q^{58} + 44 q^{60} - 4 q^{61} + 32 q^{62} - 28 q^{64} - 24 q^{65} + 32 q^{66} - 16 q^{67} - 40 q^{68} + 8 q^{69} + 16 q^{70} - 32 q^{71} - 12 q^{72} - 60 q^{73} - 20 q^{74} - 16 q^{75} - 48 q^{76} + 8 q^{77} + 48 q^{78} + 32 q^{79} + 32 q^{80} - 76 q^{81} - 8 q^{82} - 192 q^{86} + 88 q^{88} + 28 q^{89} - 48 q^{91} - 24 q^{94} + 24 q^{95} - 16 q^{97} + 268 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(555, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
555.2.j.a 555.j 185.f $76$ $4.432$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(555, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(555, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)